I'll be the first to say I don't like this guide.
First off: These are AVATARS. Notice the capitalization. In NO WAY will they be very much weaker on the day their element is weak to. They STILL have double elemental status in the area you fight them. You said against...Garuda? that you had one of Carbuncle's Searing Lights resisted for half damage.
I went on Lightsday for every fight, never had a single resist. All SLs did 210 DMG, each and every time. That's a minimum of 18 Unresisted SLs on Lightsday, but it's actually more, because the only two Avatars I beat the first time were Garuda and Leviathan.
To all you new SMNs, trying out these battles, go on Lightsday, when Carbuncle is strongest. You'll be happier you did.
Secondly, all I took was 1 Yagudo Drink, 1 Boiled Crab or Fish Mithkabob, 1 Pamama Au Lait, and 2 Ethers. I only started bringing the two Ethers after I'd already beaten Titan and Shiva, just to be on the safe side. I believe I might have brought along 1 Potion also to a few of them, only used it once. You don't need Hi-Potions at all, especially not 4 of them.
As for the rest of the guide, besides the items and the choice of day, nothing else was really wrong.
I did all the battles as a Lvl 20 SMN, Summoning Skill wasn't capped, but was at most 6 from the cap (not really a big deal as no one knows for sure what Summoning Skill really does). Never got anything higher than Protect I (from myself). Got teleported, use Protect, Aquaveil, and a barelement if it applied. Shiva doesn't cast Sleep to my knowledge. I believe they're restricted to only using abilities they'd have in your hands at 20.
I don't think you needed to make this guide. It may have helped some, but you act like you're the be all end all person when it comes to the Level 20 Mini Battles.
Didn't rate you in either direction, though, I'm pretty sure you can't rate anybody unless you have an average rating of above 3.00.
FFXI: Yzerman on Bahamut server